8 papers
Proof of Sun's conjectures on hyperbolic cosine series via the Eisenstein--Lambert method
Nikita Kalinin
We prove two conjectures of Zhi-Wei Sun concerning hyperbolic cosine Lambert series. The first one is the evaluation, for integers , of \[ S_m=\sum_{n=1}^\infty\left( \fra…
Residues of a tropical zeta function for convex domains
Nikita Kalinin, Ernesto Lupercio, Mikhail Shkolnikov
We define an -invariant tropical zeta function of a convex domain. In dimension 2 it admits boundary Dirichlet-series representation with summands…
The Directed Abelian Sandpile Model on Cylinders
Abdul Quadir, Nikita Kalinin, Ram Ramaswamy
We study the abelian sandpile model in two dimensions on a directed cylindrical lattice with periodic transverse boundary conditions in the transverse direction and dissipation at…
Continued fractions, determinant expressions, and identities
Nikita Kalinin, Takao Komatsu
In this paper, we clarified the relationship between continued fractions, determinants, and identities, making it easier to apply these methods systematically in other settings. In…
Error terms for continued fractions of and
Nikita Kalinin, Takao Komatsu
Many classical identities arise from nothing more mysterious than looking at the same object in two different ways. A number, a function, or a combinatorial object may admit severa…
CayleyPy-4: AI-Holography. Towards analogs of holographic string dualities for AI tasks
A. Chervov, F. Levkovich-Maslyuk, A. Smolensky +41
This is the fourth paper in the CayleyPy project, which applies AI methods to the exploration of large graphs. In this work, we suggest the existence of a new discrete version of h…